[EM] Approval Voting vs Instant Runoff Voting:

[Bart Ingles]

LAYTON Craig wrote:
> 
> Mike wrote:
> 
> >As I recently just finished saying here, every pairwise preference that you
> 
> >vote in Approval is reliably & fully counted. In what sense, then
> >do you claim that no one's vote counts? Or that the ordinary voter's
> >vote doesn't count?
> 
> For a while I've been saying that preferential systems standardise voting
> power, which is important in giving voters an equal say.  Approval does not
> do this.  Here is what I mean;
> 
> <please note: I'm not arguing that IRV is better than approval, simply that
> I don't find approval acceptable>
> 
> There is a four candidate race.  There may be more than four candidates, but
> only four are "contenders".  The race is very close between all four
> contenders, and opinion polls are neck and neck.
> 
> the ballots are
> A 20
> B 14
> C 13
> D 23
> AB 10
> CD 10
> BCD 5
> ABC 5
> 
> the results are
> D 38
> A 35
> B 34
> C 33
> 
> D is elected with only 38 percent of the vote.  The result is worse than an
> IRV election, in which you can at least be certain that the winner has won
> at least one pairwise contest against another candidate.  In this approval
> election, you could well be electing the Condorcet loser.  Many voters waste

You're not arguing that a voting system should "guarantee a majority
winner", are you?  You don't show any voter utilities or ratings, so
it's impossible to tell from the example above whether the voters'
strategies are good or bad.  It may be that no candidate has the support
of more than 38 percent of the voters.  Attempting to guarantee a
majority-by-fiat could produce an even worse result: a winner with
meaningful support of only 12.5% of the voters!

At least with approval voting, you can guarantee that at least 25% of
the voters either preferred the eventual winner, or were willing to vote
for the winner alongside their favorite.


> their vote, because the information available (showing the candidates equal)
> wasn't sufficient enough to tell them how many candidates they should vote
> for to maximise their voting power, assuming that ordinary voters have the
> inclination or capacity to process this information in anything other than a
> two horse race.  Relying on strategy for your voting system to work is
> highly fallable.

Relying on a complete lack of strategy is equally fallible, and
guarantees that extremely unpopular candidates will be elected in at
least some situations.

Besides, the best approval voting strategy in the situation you describe
is well known -- vote for any front-runner you consider to be "better
than average".  In a random society, this means that the typical voter
should generally vote for two candidates in a four-way race, unless the
middle candidates are substantially worse or better than expected (in
which case the voter should vote for either one or three candidates).

In a highly polarized society, where different groups dislike each other
more-or-less equally, best strategy may well be to bullet vote.  There
is no point in voting for a second choice if you don't like any of the
second choices.  Thus the winner may have as little as 25% of the vote. 
This may be an unfortunate situation, but enticing voters to make
risk-free second choices for candidates they despise is not going to
improve things.  When the electorate is highly fragmented, there is no
magical way of counting votes which will result in a winner with
majority support.


> Quite a few voters vote for only one candidate.  I don't see this as an
> exaggeration.  I'm sure that you can imagine a four candidate race where
> your utilities are such that you would bullet vote.  If you're a left-wing

Personally, sometimes I favor a third-party candidate, and sometimes I
prefer a major-party candidate.  When the former is the case, I would
expect to vote for two or more candidates; when the latter, I would
bullet vote.

If you are departing from the four-equal-frontrunner example above, then
I would expect the vast majority of voters to bullet vote, at least
present-day U.S. elections where two parties dominate.  Assuming most
voters, at least for the near future, continue to prefer major party
candidates, then I would expect them to bullet vote.  Sorry, but I
really don't see this as a problem.


> American, I guess it would be a race between a democrat, republican, reform
> and then someone even more right wing than that.  In Australia, I can
> imagine the race to be between Labor, Liberal, National and One Nation.  In
> that order, my sincere estimated utility value (out of 100) would be
> something like 100, 25, 20, 0.  It would not be unreasonable to suggest that
> I vote for only the "100" in such a scenario.

I agree -- especially since your mean utility for the four candidates is
around 36.
  
It's interesting that you were able to arrive at the correct strategy,
apparently without resorting to the math.  I suspect that most real-life
voting situations will be similarly obvious.


> The approval example isn't too unrealistic.  It could be worse.

But not as bad as with some other systems.

-Bart